This paper presents a novel approach to parts-based object recognition in the presence of occlusion. We focus on the problem of determining the pose of a 3-D object from a single 2-D image when convex parts of the object have been matched to corresponding regions in the image. We consider three types of occlusions: self-occlusion, occlusions whose locus is identified in the image, and completely arbitrary occlusions. We derive efficient algorithms for the first two cases, and characterize their performance. For the last case, we prove that the problem of finding valid poses is computationally hard, but provide an efficient, approximate algorithm. This work generalizes our previous work on region-based object recognition, which focused on the case of planar models